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<li><a class="reference internal" href="#">Post pruning decision trees with cost complexity pruning</a><ul>
<li><a class="reference internal" href="#total-impurity-of-leaves-vs-effective-alphas-of-pruned-tree">Total impurity of leaves vs effective alphas of pruned tree</a></li>
<li><a class="reference internal" href="#accuracy-vs-alpha-for-training-and-testing-sets">Accuracy vs alpha for training and testing sets</a></li>
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<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-tree-plot-cost-complexity-pruning-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
</div>
<div class="sphx-glr-example-title section" id="post-pruning-decision-trees-with-cost-complexity-pruning">
<span id="sphx-glr-auto-examples-tree-plot-cost-complexity-pruning-py"></span><h1>Post pruning decision trees with cost complexity pruning<a class="headerlink" href="#post-pruning-decision-trees-with-cost-complexity-pruning" title="Permalink to this headline">¶</a></h1>
<p>The <a class="reference internal" href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="sklearn.tree.DecisionTreeClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">DecisionTreeClassifier</span></code></a> provides parameters such as
<code class="docutils literal notranslate"><span class="pre">min_samples_leaf</span></code> and <code class="docutils literal notranslate"><span class="pre">max_depth</span></code> to prevent a tree from overfiting. Cost
complexity pruning provides another option to control the size of a tree. In
<a class="reference internal" href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="sklearn.tree.DecisionTreeClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">DecisionTreeClassifier</span></code></a>, this pruning technique is parameterized by the
cost complexity parameter, <code class="docutils literal notranslate"><span class="pre">ccp_alpha</span></code>. Greater values of <code class="docutils literal notranslate"><span class="pre">ccp_alpha</span></code>
increase the number of nodes pruned. Here we only show the effect of
<code class="docutils literal notranslate"><span class="pre">ccp_alpha</span></code> on regularizing the trees and how to choose a <code class="docutils literal notranslate"><span class="pre">ccp_alpha</span></code>
based on validation scores.</p>
<p>See also <a class="reference internal" href="../../modules/tree.html#minimal-cost-complexity-pruning"><span class="std std-ref">Minimal Cost-Complexity Pruning</span></a> for details on pruning.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_breast_cancer</span>
<span class="kn">from</span> <span class="nn">sklearn.tree</span> <span class="kn">import</span> <span class="n">DecisionTreeClassifier</span>
</pre></div>
</div>
<div class="section" id="total-impurity-of-leaves-vs-effective-alphas-of-pruned-tree">
<h2>Total impurity of leaves vs effective alphas of pruned tree<a class="headerlink" href="#total-impurity-of-leaves-vs-effective-alphas-of-pruned-tree" title="Permalink to this headline">¶</a></h2>
<p>Minimal cost complexity pruning recursively finds the node with the “weakest
link”. The weakest link is characterized by an effective alpha, where the
nodes with the smallest effective alpha are pruned first. To get an idea of
what values of <code class="docutils literal notranslate"><span class="pre">ccp_alpha</span></code> could be appropriate, scikit-learn provides
<a class="reference internal" href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier.cost_complexity_pruning_path" title="sklearn.tree.DecisionTreeClassifier.cost_complexity_pruning_path"><code class="xref py py-func docutils literal notranslate"><span class="pre">DecisionTreeClassifier.cost_complexity_pruning_path</span></code></a> that returns the
effective alphas and the corresponding total leaf impurities at each step of
the pruning process. As alpha increases, more of the tree is pruned, which
increases the total impurity of its leaves.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">load_breast_cancer</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>

<span class="n">clf</span> <span class="o">=</span> <span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">path</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">cost_complexity_pruning_path</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
<span class="n">ccp_alphas</span><span class="p">,</span> <span class="n">impurities</span> <span class="o">=</span> <span class="n">path</span><span class="o">.</span><span class="n">ccp_alphas</span><span class="p">,</span> <span class="n">path</span><span class="o">.</span><span class="n">impurities</span>
</pre></div>
</div>
<p>In the following plot, the maximum effective alpha value is removed, because
it is the trivial tree with only one node.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ccp_alphas</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">impurities</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">drawstyle</span><span class="o">=</span><span class="s2">&quot;steps-post&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;effective alpha&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;total impurity of leaves&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Total Impurity vs effective alpha for training set&quot;</span><span class="p">)</span>
</pre></div>
</div>
<p>Next, we train a decision tree using the effective alphas. The last value
in <code class="docutils literal notranslate"><span class="pre">ccp_alphas</span></code> is the alpha value that prunes the whole tree,
leaving the tree, <code class="docutils literal notranslate"><span class="pre">clfs[-1]</span></code>, with one node.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">clfs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">ccp_alpha</span> <span class="ow">in</span> <span class="n">ccp_alphas</span><span class="p">:</span>
    <span class="n">clf</span> <span class="o">=</span> <span class="n">DecisionTreeClassifier</span><span class="p">(</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">ccp_alpha</span><span class="o">=</span><span class="n">ccp_alpha</span><span class="p">)</span>
    <span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
    <span class="n">clfs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">clf</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Number of nodes in the last tree is: </span><span class="si">{}</span><span class="s2"> with ccp_alpha: </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
      <span class="n">clfs</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">tree_</span><span class="o">.</span><span class="n">node_count</span><span class="p">,</span> <span class="n">ccp_alphas</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]))</span>
</pre></div>
</div>
<p>For the remainder of this example, we remove the last element in
<code class="docutils literal notranslate"><span class="pre">clfs</span></code> and <code class="docutils literal notranslate"><span class="pre">ccp_alphas</span></code>, because it is the trivial tree with only one
node. Here we show that the number of nodes and tree depth decreases as alpha
increases.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">clfs</span> <span class="o">=</span> <span class="n">clfs</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">ccp_alphas</span> <span class="o">=</span> <span class="n">ccp_alphas</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>

<span class="n">node_counts</span> <span class="o">=</span> <span class="p">[</span><span class="n">clf</span><span class="o">.</span><span class="n">tree_</span><span class="o">.</span><span class="n">node_count</span> <span class="k">for</span> <span class="n">clf</span> <span class="ow">in</span> <span class="n">clfs</span><span class="p">]</span>
<span class="n">depth</span> <span class="o">=</span> <span class="p">[</span><span class="n">clf</span><span class="o">.</span><span class="n">tree_</span><span class="o">.</span><span class="n">max_depth</span> <span class="k">for</span> <span class="n">clf</span> <span class="ow">in</span> <span class="n">clfs</span><span class="p">]</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ccp_alphas</span><span class="p">,</span> <span class="n">node_counts</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">drawstyle</span><span class="o">=</span><span class="s2">&quot;steps-post&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;alpha&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;number of nodes&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Number of nodes vs alpha&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ccp_alphas</span><span class="p">,</span> <span class="n">depth</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">drawstyle</span><span class="o">=</span><span class="s2">&quot;steps-post&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;alpha&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;depth of tree&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Depth vs alpha&quot;</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="section" id="accuracy-vs-alpha-for-training-and-testing-sets">
<h2>Accuracy vs alpha for training and testing sets<a class="headerlink" href="#accuracy-vs-alpha-for-training-and-testing-sets" title="Permalink to this headline">¶</a></h2>
<p>When <code class="docutils literal notranslate"><span class="pre">ccp_alpha</span></code> is set to zero and keeping the other default parameters
of <a class="reference internal" href="../../modules/generated/sklearn.tree.DecisionTreeClassifier.html#sklearn.tree.DecisionTreeClassifier" title="sklearn.tree.DecisionTreeClassifier"><code class="xref py py-class docutils literal notranslate"><span class="pre">DecisionTreeClassifier</span></code></a>, the tree overfits, leading to
a 100% training accuracy and 88% testing accuracy. As alpha increases, more
of the tree is pruned, thus creating a decision tree that generalizes better.
In this example, setting <code class="docutils literal notranslate"><span class="pre">ccp_alpha=0.015</span></code> maximizes the testing accuracy.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">train_scores</span> <span class="o">=</span> <span class="p">[</span><span class="n">clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span> <span class="k">for</span> <span class="n">clf</span> <span class="ow">in</span> <span class="n">clfs</span><span class="p">]</span>
<span class="n">test_scores</span> <span class="o">=</span> <span class="p">[</span><span class="n">clf</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)</span> <span class="k">for</span> <span class="n">clf</span> <span class="ow">in</span> <span class="n">clfs</span><span class="p">]</span>

<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;alpha&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;accuracy&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Accuracy vs alpha for training and testing sets&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ccp_alphas</span><span class="p">,</span> <span class="n">train_scores</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;train&quot;</span><span class="p">,</span>
        <span class="n">drawstyle</span><span class="o">=</span><span class="s2">&quot;steps-post&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ccp_alphas</span><span class="p">,</span> <span class="n">test_scores</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;test&quot;</span><span class="p">,</span>
        <span class="n">drawstyle</span><span class="o">=</span><span class="s2">&quot;steps-post&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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